On the 2PN periastron precession of the Double Pulsar PSR J0737-3039A/B

TL;DR

This paper derives an analytical expression for the 2PN periastron precession in binary pulsars, clarifying previous calculations and highlighting its significance in testing general relativity with the Double Pulsar PSR J0737-3039A/B.

Contribution

It provides a corrected and detailed formula for the 2PN periastron precession applicable to binary pulsars, including its dependence on initial orbital phase.

Findings

The 2PN precession range is between -0.00080°/yr and -0.00045°/yr.

The derived formula aligns with Damour and Schäfer's parameterization.

Corrects past errors in 2PN precession calculations.

Abstract

One of the post-Keplerian (PK) parameters determined in timing analyses of several binary pulsars is the fractional periastron advance per orbit $k^\mathrm{PK}$. Along with other PK parameters, it is used in testing general relativity once it is translated into the periastron precession $\dot\omega^\mathrm{PK}$. It was recently remarked that the periastron $\omega$ of PSR J0737--3039A/B may be used to measure/constrain the moment of inertia of A through the extraction of the general relativistic Lense-Thirring precession $\dot\omega^\mathrm{LT,\,A}\simeq -0.00060^\circ\,\mathrm{yr}^{-1}$ from the experimentally determined periastron rate $\dot\omega_\mathrm{obs}$ provided that the other post--Newtonian (PN) contributions to $\dot\omega_\mathrm{exp}$ can be accurately modeled. Among them, the 2PN one seems to be of the same order of magnitude of $\dot\omega^\mathrm{LT,\,A}$. An analytical expression of the total 2PN periastron precession $\dot\omega^\mathrm{2PN}$ in terms of the osculating Keplerian orbital elements, valid not only for binary pulsars, is provided elucidating the subtleties implied in correctly calculating it from $k^\mathrm{1PN}+k^\mathrm{2PN}$ and correcting some past errors by the present author. The formula for $\dot\omega^\mathrm{2PN}$ is demonstrated to be equivalent to that obtainable from $k^\mathrm{1PN}+k^\mathrm{2PN}$ by Damour and Sch\"afer expressed in the Damour-Deruelle (DD) parameterization. $\dot\omega^\mathrm{2PN}$ actually depends on the initial orbital phase, hidden in the DD picture, so that $-0.00080^\circ\,\mathrm{yr}^{-1} \leq\dot\omega^\mathrm{2PN}\leq -0.00045^\circ\,\mathrm{\,yr}^{-1}$. A recently released prediction of $\dot\omega^\mathrm{2PN}$ for \psrab\, is discussed.